scholarly journals A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dimitri Mugnai ◽  
Kanishka Perera ◽  
Edoardo Proietti Lippi
Keyword(s):  
Boundary Conditions ◽  
Morse Theory ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Priori Estimates ◽  
Variational Tools

<p style='text-indent:20px;'>We first prove that solutions of fractional <i>p</i>-Laplacian problems with nonlocal Neumann boundary conditions are bounded and then we apply such a result to study some resonant problems by means of variational tools and Morse theory.</p>

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals On the Neumann Problem for Monge-Ampére Type Equations

2016 ◽  
Vol 68 (6) ◽  
pp. 1334-1361 ◽  
Author(s):  
Feida Jiang ◽  
Neil S. Trudinger ◽  
Ni Xiang
Keyword(s):  
Global Regularity ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Neumann Boundary ◽  
Natural Conditions ◽  
Priori Estimates ◽  
The Neumann Problem ◽  
Monge Ampere ◽  
Oblique Boundary

AbstractIn this paper, we study the global regularity for regular Monge-Ampère type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Ampère case by Lions, Trudinger, and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger, and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.

scholarly journals A QUANTUM TRANSMITTING SCHRÖDINGER–POISSON SYSTEM

2004 ◽  
Vol 16 (03) ◽  
pp. 281-330 ◽  
Author(s):  
M. BARO ◽  
H.-CHR. KAISER ◽  
H. NEIDHARDT ◽  
J. REHBERG
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Real Axis ◽  
A Priori Estimates ◽  
A Priori ◽  
Poisson System ◽  
Transparent Boundary Conditions ◽  
Bounded Interval ◽  
Zero Current ◽  
Priori Estimates

We study a stationary Schrödinger–Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows us to model a non-zero current through the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

scholarly journals An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Moussa Zakari Djibibe ◽  
Kokou Tcharie ◽  
N. Iossifovich Yurchuk
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
A Priori Estimates ◽  
A Priori ◽  
Energy Inequality ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Function Spaces ◽  
Priori Estimates ◽  
Singular Parabolic Equations

The aim of this paper is to establish a priori estimates of the following nonlocal boundary conditions mixed problem for parabolic equation: ∂v/∂t-(a(t)/x2)(∂/∂x)(x2∂v/∂x)+b(x,t)v=g(x,t), v(x, 0)=ψ(x), 0≤x≤ℓ, v(ℓ, t)=E(t), 0≤t≤T, ∫0ℓx3v(x,t)dx=G(t), 0≤t≤ℓ. It is important to know that a priori estimates established in nonclassical function spaces is a necessary tool to prove the uniqueness of a strong solution of the studied problems.

scholarly journals A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONS

2017 ◽  
Vol 17 (8) ◽  
pp. 102-107
Author(s):  
E.A. Utkina
Keyword(s):  
Boundary Conditions ◽  
Unknown Function ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Fredholm Equations ◽  
Priori Estimates ◽  
Linear Hyperbolic Equations

A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.

scholarly journals Infinitely many solutions for mixed Dirichlet-Neumann problems driven by the (p,q)-laplace operator

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4603-4611 ◽  
Author(s):  
Francesca Vetro
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Nonlinear Problem ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Infinitely Many Solutions ◽  
Neumann Problems ◽  
Reaction Term ◽  
Variational Tools

We study a nonlinear problem with mixed Dirichlet-Neumann boundary conditions involving the p-Laplace operator and the q-Laplace operator ((p,q)-Laplace operator). Using variational tools and appropriate hypotheses on the behavior either at infinity or at zero of the reaction term, we prove that such a problem has infinitely many solutions.

An inverse problem for the KdV equation with Neumann boundary measured data

2018 ◽  
Vol 26 (1) ◽  
pp. 133-151 ◽  
Author(s):  
Sakthivel Kumarasamy ◽  
Alemdar Hasanov
Keyword(s):  
Inverse Problem ◽  
A Priori Estimates ◽  
Kdv Equation ◽  
A Priori ◽  
Gradient Methods ◽  
Neumann Boundary ◽  
Sobolev Norm ◽  
Minimum Problem ◽  
Existence Of A Solution ◽  
Priori Estimates

AbstractIn this paper, we consider an inverse coefficient problem for the linearized Korteweg–de Vries (KdV) equation {u_{t}+u_{xxx}+(c(x)u)_{x}=0}, with homogeneous boundary conditions {u(0,t)=u(1,t)=u_{x}(1,t)=0}, when the Neumann data{g(t):=u_{x}(0,t)}, {t\in(0,T)}, is given as an available measured output at the boundary {x=0}. The inverse problem is formulated as a minimum problem for the regularized Tikhonov functional {\mathcal{J}_{\alpha}(c)=\frac{1}{2}\|u_{x}(0,\cdot\,;c)-g\|^{2}_{L^{2}(0,T)}+% \frac{\alpha}{2}\|c^{\prime}\|^{2}_{L^{2}(0,1)}} with Sobolev norm. Based on a priori estimates for the weak and regular weak solutions of the direct and adjoint problems, it is proved that the input-output operator is compact, which shows the ill-posedness of the inverse problem. Then Fréchet differentiability of the Tikhonov functional and Lipschitz continuity of the Fréchet gradient are proved. It is shown that the last result allows us to use an important advantage of gradient methods when the functional is from the class {C^{1,1}(\mathcal{M})}. In the final part, an existence of a solution of the minimum problem for the regularized Tikhonov functional {\mathcal{J}_{\alpha}(c)} is proved.

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